Not sure what airlines you’re taking but I took SQ for my flight to Korea last year Oct (also midnight flight). 1. I packed 3 bottles of 180ml formula (premade as my baby only drinks cold milk), then 3 empty bottles to make milk on board (ask FA for water). I also brought along a 330ml water bottle for my lo. They didn’t check or stop me as I was carrying LO. At Korea’s airport, they did ask me what is inside the cooler bag and I told them it’s baby formula and they just let me pass, sg side didn’t ask. However for other countries, it depends. My friend got asked to dump her formula when she came back from Japan even when baby is with her. 2. Can bring pouched food for baby (but they probably won’t be able to heat up for you), safer to bring your own (for spare) in case baby dislike on board food (which most likely is gerber’s puree for infants). 3. Can’t advise as my lo is 22m when we took the flight. If baby is not on pacifier then try to let baby’s feeding time align with take off and landing time so that it can help to relieve some pressure from the ears.
For water in thermos or baby’s formula idt they have limit as long as its for the baby and baby is with you. I brought 550 of hot water in thermos in my diaper bag.